Question

Easton and Eli go to the movie theater and purchase refreshments for their friends.

Answer 1

Answer:

 Price of one bag of popcorn: $9.5

Price of one drink: $5.5

Step-by-step explanation:

Let be "b" the price in dollars of a bag of popcorn and "d" the price in dollars of a drink.

You know that the total amount of money Easton spends on on 9 bags of popcorn and 6 drinks, is $118.50. Then,this can be represented with the following equation:

$9b+6d=118.50$

Knowing that Eli spends  $83.50 on 3 bags of popcorn and 10 drinks, you can write the second equation:

$3b+10d=83.50$

Then, the System of equations is:

$\left \{ {{9b+6d=118.50} \atop {3b+10d=83.50}} \right.$

You can use the Elimination methot to solve it:

1. Multiply the second equation by -3.

2. Add both equations.

3. Solve for "d"

Then, you get:

$\left \{ {{9b+6d=118.50} \atop {-9b-30d=-250.5}} \right\\............................\\-24d=-132\\\\d=5.5$

4. You can subsitute "d" into the second equation and solve for "b":

$3b+10(5.5)=83.50\\\\3b=83.50-55\\\\b=9.5$